Uniform Price Auctions: Equilibria and Efficiency

We present our results on Uniform Price Auctions, one of the standard sealed-bid multi-unit auction formats, for selling multiple identical units of a single good to multi-demand bidders. Contrary to the truthful and economically efficient multi-unit Vickrey auction, the Uniform Price Auction encourages strategic bidding and is socially inefficient in general, partly due to a ”Demand Reduction” effect; bidders tend to bid for fewer (identical) units, so as to receive them at a lower uniform price. Despite its inefficiency, the uniform pricing rule is widely popular by its appeal to the natural anticipation, that identical items should be identically priced. Application domains of its variants include sales of U.S. Treasury bonds to investors, trade exchanges over the internet facilitated by popular online brokers, allocation of radio spectrum licenses etc. In this work we study equilibria of the Uniform Price Auction in undominated strategies. We characterize a class of undominated pure Nash equilibria and quantify the social inefficiency of pure and (mixed) Bayes-Nash equilibria by means of bounds on the Price of Anarchy.